236 lines
7.1 KiB
C
236 lines
7.1 KiB
C
|
/*=============================================================================
|
||
|
|
|
||
|
|
This file is part of FLINT.
|
||
|
|
|
||
|
|
FLINT is free software; you can redistribute it and/or modify
|
||
|
|
it under the terms of the GNU General Public License as published by
|
||
|
|
the Free Software Foundation; either version 2 of the License, or
|
||
|
|
(at your option) any later version.
|
||
|
|
|
||
|
|
FLINT is distributed in the hope that it will be useful,
|
||
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||
|
|
GNU General Public License for more details.
|
||
|
|
|
||
|
|
You should have received a copy of the GNU General Public License
|
||
|
|
along with FLINT; if not, write to the Free Software
|
||
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||
|
|
|
||
|
|
=============================================================================*/
|
||
|
|
/******************************************************************************
|
||
|
|
|
||
|
|
Copyright (C) 2009 William Hart
|
||
|
|
Copyright (C) 2010 Sebastian Pancratz
|
||
|
|
|
||
|
|
******************************************************************************/
|
||
|
|
|
||
|
|
#include <stdio.h>
|
||
|
|
#include <stdlib.h>
|
||
|
|
#include <gmp.h>
|
||
|
|
#include "flint.h"
|
||
|
|
#include "fmpz.h"
|
||
|
|
#include "fmpz_poly.h"
|
||
|
|
#include "ulong_extras.h"
|
||
|
|
|
||
|
|
/*
|
||
|
|
Tests whether the polynomial is suitably normalised for the
|
||
|
|
result of a GCD operation, that is, whether it's leading
|
||
|
|
coefficient is non-negative.
|
||
|
|
*/
|
||
|
|
static
|
||
|
|
int _t_gcd_is_canonical(const fmpz_poly_t poly)
|
||
|
|
{
|
||
|
|
return fmpz_poly_is_zero(poly) || (fmpz_sgn(fmpz_poly_lead(poly)) > 0);
|
||
|
|
}
|
||
|
|
|
||
|
|
int
|
||
|
|
main(void)
|
||
|
|
{
|
||
|
|
int i, result, d1, d2;
|
||
|
|
FLINT_TEST_INIT(state);
|
||
|
|
|
||
|
|
flint_printf("gcd_heuristic....");
|
||
|
|
fflush(stdout);
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
/* Check aliasing of a and b */
|
||
|
|
for (i = 0; i < 100 * flint_test_multiplier(); i++)
|
||
|
|
{
|
||
|
|
fmpz_poly_t a, b, c;
|
||
|
|
|
||
|
|
fmpz_poly_init(a);
|
||
|
|
fmpz_poly_init(b);
|
||
|
|
fmpz_poly_init(c);
|
||
|
|
fmpz_poly_randtest(b, state, n_randint(state, 40), 80);
|
||
|
|
fmpz_poly_randtest(c, state, n_randint(state, 40), 80);
|
||
|
|
|
||
|
|
d1 = fmpz_poly_gcd_heuristic(a, b, c);
|
||
|
|
d2 = fmpz_poly_gcd_heuristic(b, b, c);
|
||
|
|
|
||
|
|
result = ((d1 == 0 && d2 == 0) || (fmpz_poly_equal(a, b)
|
||
|
|
&& _t_gcd_is_canonical(a)));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (aliasing a and b):\n");
|
||
|
|
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
|
||
|
|
flint_printf("b = "), fmpz_poly_print(b), flint_printf("\n\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_poly_clear(a);
|
||
|
|
fmpz_poly_clear(b);
|
||
|
|
fmpz_poly_clear(c);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Check aliasing of a and c */
|
||
|
|
for (i = 0; i < 100 * flint_test_multiplier(); i++)
|
||
|
|
{
|
||
|
|
fmpz_poly_t a, b, c;
|
||
|
|
|
||
|
|
fmpz_poly_init(a);
|
||
|
|
fmpz_poly_init(b);
|
||
|
|
fmpz_poly_init(c);
|
||
|
|
fmpz_poly_randtest(b, state, n_randint(state, 40), 80);
|
||
|
|
fmpz_poly_randtest(c, state, n_randint(state, 40), 80);
|
||
|
|
|
||
|
|
d1 = fmpz_poly_gcd_heuristic(a, b, c);
|
||
|
|
d2 = fmpz_poly_gcd_heuristic(c, b, c);
|
||
|
|
|
||
|
|
result = ((d1 == 0 && d2 == 0) || (fmpz_poly_equal(a, c)
|
||
|
|
&& _t_gcd_is_canonical(a)));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (aliasing a and c):\n");
|
||
|
|
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
|
||
|
|
flint_printf("c = "), fmpz_poly_print(c), flint_printf("\n\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_poly_clear(a);
|
||
|
|
fmpz_poly_clear(b);
|
||
|
|
fmpz_poly_clear(c);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Check that a divides GCD(af, ag) */
|
||
|
|
for (i = 0; i < 300 * flint_test_multiplier(); i++)
|
||
|
|
{
|
||
|
|
fmpz_poly_t a, d, f, g, q, r;
|
||
|
|
|
||
|
|
fmpz_poly_init(a);
|
||
|
|
fmpz_poly_init(d);
|
||
|
|
fmpz_poly_init(f);
|
||
|
|
fmpz_poly_init(g);
|
||
|
|
fmpz_poly_init(q);
|
||
|
|
fmpz_poly_init(r);
|
||
|
|
fmpz_poly_randtest_not_zero(a, state, n_randint(state, 100) + 1, 40);
|
||
|
|
fmpz_poly_randtest(f, state, n_randint(state, 100), 40);
|
||
|
|
fmpz_poly_randtest(g, state, n_randint(state, 100), 40);
|
||
|
|
|
||
|
|
fmpz_poly_mul(f, a, f);
|
||
|
|
fmpz_poly_mul(g, a, g);
|
||
|
|
d1 = fmpz_poly_gcd_heuristic(d, f, g);
|
||
|
|
|
||
|
|
if (d1)
|
||
|
|
{
|
||
|
|
fmpz_poly_divrem_divconquer(q, r, d, a);
|
||
|
|
|
||
|
|
result = fmpz_poly_is_zero(r) && _t_gcd_is_canonical(d);
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (check a | gcd(af, ag)):\n");
|
||
|
|
flint_printf("f = "), fmpz_poly_print(f), flint_printf("\n");
|
||
|
|
flint_printf("g = "), fmpz_poly_print(g), flint_printf("\n");
|
||
|
|
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n");
|
||
|
|
flint_printf("d = "), fmpz_poly_print(d), flint_printf("\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_poly_clear(a);
|
||
|
|
fmpz_poly_clear(d);
|
||
|
|
fmpz_poly_clear(f);
|
||
|
|
fmpz_poly_clear(g);
|
||
|
|
fmpz_poly_clear(q);
|
||
|
|
fmpz_poly_clear(r);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Check that a == GCD(af, ag) when GCD(f, g) = 1 */
|
||
|
|
for (i = 0; i < 300 * flint_test_multiplier(); i++)
|
||
|
|
{
|
||
|
|
fmpz_poly_t a, d, f, g, q, r;
|
||
|
|
|
||
|
|
fmpz_poly_init(a);
|
||
|
|
fmpz_poly_init(d);
|
||
|
|
fmpz_poly_init(f);
|
||
|
|
fmpz_poly_init(g);
|
||
|
|
fmpz_poly_init(q);
|
||
|
|
fmpz_poly_init(r);
|
||
|
|
fmpz_poly_randtest_not_zero(a, state, n_randint(state, 100) + 1, 200);
|
||
|
|
do {
|
||
|
|
fmpz_poly_randtest(f, state, n_randint(state, 100), 200);
|
||
|
|
fmpz_poly_randtest(g, state, n_randint(state, 100), 200);
|
||
|
|
fmpz_poly_gcd_heuristic(d, f, g);
|
||
|
|
} while (!(d->length == 1 && fmpz_is_one(d->coeffs)));
|
||
|
|
|
||
|
|
fmpz_poly_mul(f, a, f);
|
||
|
|
fmpz_poly_mul(g, a, g);
|
||
|
|
d1 = fmpz_poly_gcd_heuristic(d, f, g);
|
||
|
|
|
||
|
|
if (d1)
|
||
|
|
{
|
||
|
|
if (!_t_gcd_is_canonical(a)) fmpz_poly_neg(a, a);
|
||
|
|
|
||
|
|
result = fmpz_poly_equal(d, a) && _t_gcd_is_canonical(d);
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (check a == gcd(af, ag) when gcd(f, g) = 1):\n");
|
||
|
|
flint_printf("f = "), fmpz_poly_print(f), flint_printf("\n");
|
||
|
|
flint_printf("g = "), fmpz_poly_print(g), flint_printf("\n");
|
||
|
|
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n");
|
||
|
|
flint_printf("d = "), fmpz_poly_print(d), flint_printf("\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_poly_clear(a);
|
||
|
|
fmpz_poly_clear(d);
|
||
|
|
fmpz_poly_clear(f);
|
||
|
|
fmpz_poly_clear(g);
|
||
|
|
fmpz_poly_clear(q);
|
||
|
|
fmpz_poly_clear(r);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Sebastian's test case */
|
||
|
|
{
|
||
|
|
fmpz_poly_t a, b, d;
|
||
|
|
|
||
|
|
fmpz_poly_init(a);
|
||
|
|
fmpz_poly_init(b);
|
||
|
|
fmpz_poly_init(d);
|
||
|
|
|
||
|
|
fmpz_poly_set_coeff_ui(b, 2, 1);
|
||
|
|
fmpz_poly_set_coeff_si(a, 0, -32);
|
||
|
|
fmpz_poly_set_coeff_si(a, 1, 24);
|
||
|
|
|
||
|
|
fmpz_poly_gcd_heuristic(d, a, b);
|
||
|
|
|
||
|
|
result = (d->length == 1 && fmpz_is_one(d->coeffs));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (check 1 == gcd(x^2, 24*x - 32):\n");
|
||
|
|
fmpz_poly_print(d); flint_printf("\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_poly_clear(a);
|
||
|
|
fmpz_poly_clear(b);
|
||
|
|
fmpz_poly_clear(d);
|
||
|
|
}
|
||
|
|
|
||
|
|
FLINT_TEST_CLEANUP(state);
|
||
|
|
|
||
|
|
flint_printf("PASS\n");
|
||
|
|
return 0;
|
||
|
|
}
|